Fourier-matching pseudospectral modal method for diffraction gratings

Abstract

A Fourier-matching pseudospectral modal method [PSMM(f)] is developed for analyzing lamellar diffraction gratings or grating stacks. A Chebyshev pseudospectral method is first used to accurately calculate the eigenmodes of the grating layers, and then the Fourier coefficients are matched at the interfaces between the layers. Compared with an existing pseudospectral modal method based on point matching, the PSMM(f) is more robust and accurate. The method performs better than the standard Fourier modal method for gratings involving metals.

High order integral equation method for diffraction gratings

“…The first example was previously analyzed by the FMM and other numerical modal methods [14,17]. It is the dielectric lamellar grating shown in Fig.…”

“…For the conical diffraction case, the procedure is similar, but the interface condition [Eq. (17)] is vectorial, thus the modified NtD map of Ω 2 relates φj Σ 1 and φj Σ 2 with uj Σ 1 and uj Σ 2 . The boundaries of Ω 21 , Ω 22 , and Ω 1 consist of eight, four, and six smooth segments, respectively.…”

“…Efficient numerical methods are needed to analyze the diffraction and scattering of light by these periodic structures. Existing numerical methods for diffraction gratings include general-purpose methods such as the finitedifference time-domain (FDTD) method and the finite element method (FEM) [3], and more special methods such as the analytic modal method [4][5][6][7], numerical modal methods [8][9][10][11][12][13][14][15][16][17][18], the boundary integral equation (BIE) methods [19][20][21][22][23][24][25][26][27][28], etc. Although FDTD and FEM are extremely versatile, they are typically less efficient than the special methods.…”

Iterative approach as alternative to S-matrix in modal methods

“…Eigenmodes may be computed also by finite-difference approach 9,23 or by pseudospectral methods 24,25 .…”

“…In addition, determination + с and − c % opens the way to straightforward and stable calculation of the field within each layer avoiding computationally-intensive operations with partial S-matrices such as those proposed in [24]. By using the variables (20), the system has no exponentially large numbers: …”